% Be sure to set up BNT with these commands:
%addpath /net/hc283/yaner/work/bayes/BNT
%add_BNT_to_path

% The burglary example from Russell and Norvig, section 15.2
% illustrated in figure 15.2. Different sorts of inferences are
% discussed in section 15.3

% the DAG
dag = zeros(N,N);
B = 1; E = 2; A = 3; JC = 4; MC = 5;
dag([B,E],A) = 1;
dag(A,[JC,MC]) = 1;

% the actual belief net
node_sizes = 2*ones(1,N);
bnet = mk_bnet(dag, node_sizes, 'names', {'B','E','A','JC','MC'});

% the conditional probability tables (CPTs)
false = 1; true = 2;

% B | P(B)
% --------
% F | .999
% T | .001
bnet.CPD{B} = tabular_CPD(bnet, B, [.999, .001]);

% E | P(E)
% --------
% F | .998
% T | .002
bnet.CPD{E} = tabular_CPD(bnet, E, [.998, .002]);

% B E | A | P(A|B,E)
% ------------------
% F F | F | .999
% T F | F | .06
% F T | F | .71
% T T | F | .05
% F F | T | .001
% T F | T | .94
% F T | T | .29
% T T | T | .95
bnet.CPD{A} = tabular_CPD(bnet, A, [.999, .06, .71, .05, .001, .94, .29, .95]);

% A | JC | P(JC|A)
% ----------------
% F | F  | .95
% T | F  | .10
% F | T  | .05
% T | T  | .90
bnet.CPD{JC} = tabular_CPD(bnet, JC, [.95, .10, .05, .90]);

% A | MC | P(MC|A)
% ----------------
% F | F  | .99
% T | F  | .30
% F | T  | .01
% T | T  | .70
bnet.CPD{MC} = tabular_CPD(bnet, MC, [.99, .30, .01, .70]);

% Inference (using Junction Trees, an exact inference method that
% works on any static belief net)
engine = jtree_inf_engine(bnet);

% Diagnostic inference: P(B|JC)
evidence = cell(1,N);
evidence{JC} = true;
[engine, loglik] = enter_evidence(engine, evidence);
marg = marginal_nodes(engine, B);
marg.T(true) % returns P(B|JC), the answer

% Causal inference: P(MC|B)
evidence = cell(1,N);
evidence{B} = true;
[engine, loglik] = enter_evidence(engine, evidence);
marg = marginal_nodes(engine, MC);
marg.T(true) % returns P(MC|B), the answer

% Simple Intercausal inference: P(B|E)
evidence = cell(1,N);
evidence{E} = true;
[engine, loglik] = enter_evidence(engine, evidence);
marg = marginal_nodes(engine, B);
marg.T(true) % returns P(B|E)

% More interesting intercausal inference: P(B|A) first, then P(B|A,E)
evidence = cell(1,N);
evidence{A} = true;
[engine, loglik] = enter_evidence(engine, evidence);
marg = marginal_nodes(engine, B);
marg.T(true) % returns P(B|A)
% now the actual intercausal inference
evidence{E} = true;
[engine, loglik] = enter_evidence(engine, evidence);
marg = marginal_nodes(engine, B);
marg.T(true) % returns P(B|A,E)
% the probability goes down; the earthquake "explains away" the alarm.